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GDMSeminar: Abstracts of the Talks (2021/2)

Alejandro Cabrera (UFRJ, Rio de Janeiro)

Dirac structures for infinite dimensional geometries and applications

Tuesday, Fabruary 2, 2021, 16:00 GMT

Abstract: In this talk, we first review the notion of Dirac structures and their role substituting Poisson brackets in systems with constraints. We then consider Dirac structures on infinite dimensional manifolds and highlight the advantages of this notion to encode geometric structures, including Poisson structures, in this setting. Finally, we show how these structures can be reduced from infinite to finite dimensions and provide an application related to gauge theory on surfaces. This is joint work with M. Gualtieri and E. Meinrenken. At the end of the talk, we will discuss other possible applications related to discretization of continuous systems.